In 3GPP Long Term Evolution (LTE) (3GPP TS36.211 v8.2.0, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation (Release 8)”), Single Carrier Frequency Division Multiple Access (SC-FDMA) is adopted as uplink multiple access scheme in the form of Discrete Fourier Transform-Spread Orthogonal Frequency Domain Multiplexing (DFT-S-OFDM).
The main advantage with SC-FDMA is the fact that said access scheme has low Peak-to-Average Power Ratio (PAPR) compared with OFDMA. Low PAPR reduces the necessary dynamic range of Power Amplifiers (PAs), and therefore improves the efficiency of PAs, i.e. cell coverage can be extended with the same transmission power.
FIG. 1 shows the transmitter structure for DFT-S-OFDM. Block of M complex modulated symbols xn, n=0, 1, . . . , M−1, is transformed by a Discrete Fourier Transform (DFT) and results in M spectrum coefficients Xk where,
                                          X            k                    =                                    ∑                              n                =                0                                            M                -                1                                      ⁢                                                  ⁢                                          x                n                            ⁢                              ⅇ                                                      -                    j                                    ⁢                                                                          ⁢                  2                  ⁢                  π                  ⁢                                      nk                    M                                                                                      ,                  k          =          0                ,        1        ,        …        ⁢                                  ,                  M          -          1.                                    (        1        )            The output from the DFT is mapped on equidistant sub-carriers lk=l0+kL, where l0 is a frequency offset, and L is an integer larger than or equal to 1 (in LTE uplink, L=1). All other inputs to the N-point Inverse Fast Fourier Transform (IFFT) are set to zero. The output of the IFFT, yn, is given by,
                                          y            n                    =                                    1              M                        ⁢                                          ∑                                  k                  =                  0                                                  M                  -                  1                                            ⁢                                                          ⁢                                                X                  k                                ⁢                                  ⅇ                                                            -                      j2π                                        ⁢                                                                  nl                        k                                            N                                                                                                          ,                  n          =          0                ,        1        ,        …        ⁢                                  ,                  N          -          1                                    (        2        )            Finally, a cyclic prefix is inserted, wherein the insertion of the cyclic prefix does not change the PAPR of the signal.
In LTE uplink, there is only one transmit antenna working at a certain time slot. In order to further optimize and/or improve uplink performance such as e.g. peak data rate, average spectrum efficiency and cell-edge user throughput it has been suggested to increase the number of transmit antennas to four in the uplink, a fact which has been defined in the requirements of LTE-Advanced (3GPP TR36.913 v1.0.0, “Requirements for Further Advancements for E-UTRA (LTE-Advanced) (Release 8)”), hence four transmit antennas in the uplink will therefore be available.
For wireless communication systems having multiple antennas at the transmitter, transmit diversity scheme is a promising candidate to be used to improve performance of the system. Furthermore, transmit diversity schemes usually work in open loop mode, and therefore no feedback information is needed in such schemes. For example, for high speed User Equipments (UEs) in low geometry scenario, open loop spatial multiplexing does not work well because of the low geometry. Also, closed loop beam-forming is not suited for these type of scenarios as Precoding Matrix Indictor (PMI) feedback can not track the channel variations accurately; open loop transmit diversity may therefore be the only candidate to improve the communication reliability in an efficient manner.
Because of the benefits of open loop transmit diversity schemes, such schemes have been widely used in many current standards, such as WCDMA, WiMax, LTE, etc. In LTE-Advanced, four transmit antennas in the uplink will be available, and similarly open loop four antenna transmit diversity scheme should be considered for improving the performance of the system in the uplink.
In LTE downlink, the combination of Space Frequency Block Coding (SFBC) and Frequency Switched Transmit Diversity (FSTD) is defined for a four transmit antennas open loop transmit diversity scheme, which is usually called SFBC+FSTD. The encoding matrix for SFBC+FSTD in the LTE downlink is,
                              Antenna          ↓                                    (                                                                                          x                      0                                                                                                  x                      1                                                                            0                                                        0                                                                                        0                                                        0                                                                              x                      2                                                                                                  x                      3                                                                                                                                  -                                              x                        1                        *                                                                                                                        x                      0                      *                                                                            0                                                        0                                                                                        0                                                        0                                                                              -                                              x                        3                        *                                                                                                                        x                      2                      *                                                                                  )                                      →              Frequency                                      ,                            (        3        )            where the four rows of the encoding matrix represent four transmit antennas, and the four columns represent four sub-carriers which should be as consecutive as possible in the frequency domain to keep the orthogonal structure.
The structure above means that x0, x1 are separately transmitted at frequencies f1 and f2 (in the form of sub-carrier index) of antenna 1, and −x*1, x*0 are transmitted at frequencies f1 and f2 of antenna 3; while x2, x3 are transmitted at frequencies f3 and f4 of antenna 2, and −x*3, x*2 are transmitted at frequencies f3 and f4 of antenna 4.
The operation
         (                                        X            0                                                X            1                                                            -                          X              1              *                                                            X            0            *                                )  is called SFBC, which means that X0, X1 are transmitted from sub-carrier k1 and k2 of antenna 1, and −X*1, X*0 are simultaneously transmitted from sub-carrier k1 and k2 of antenna 2. Hence, it can be observed that the encoding matrix shown in (3) actually consists of two SFBCs as,
                                                   (                                                                                x                    0                                                                                        x                    1                                                                                                                    -                                          x                      1                      *                                                                                                            x                    0                    *                                                                        )                    ⁢                                                                 (                                                                                                    x                        2                                                                                                            x                        3                                                                                                                                                -                                                  x                          3                          *                                                                                                                                    x                        2                        *                                                                                            )                            .                                                          (        4        )            The first SFBC is transmitted from sub-carrier k1 and k2 of antenna 1 and 3 respectively, and the second SFBC is switched to the other two sub-carriers k3 and k4 of antenna 2 and 4. In LTE downlink, the density of reference signals used for channel estimation is different over the four transmit antennas. The first and the second antenna have the same reference signal density and the density for these antennas is larger than for the third and the fourth antenna. In order to balance the performance of the two SFBCs, it is suggested that the first SFBC is transmitted from antenna 1 and 3, and the second SFBC is transmitted from antenna 2 and 4. However for clarity of description and without loss of generality, in the remaining part of this document the first SFBC is transmitted from antenna 1 and antenna 2 respectively, and the second SFBC is transmitted from antenna 3 and antenna 4, respectively.
In LTE downlink, some downlink control channels (e.g. physical downlink control channel and physical broadcast channel) use SFBC+FSTD to improve detection performance; in addition, SFBC+FSTD is also used for downlink shared channels in low SNR or high speed scenarios. When designing four antenna transmit diversity schemes in the uplink, the PAPR issue of the transmit diversity scheme has to be addressed.
If the current downlink SFBC+FSTD is directly used for uplink transmissions as a transmit diversity scheme for four antennas along with DFT-S-OFDM the frame structure will be as shown in FIG. 2. Block of M DFT samples Xk, k=1, 2, . . . , M are encoded with SFBC+FSTD,
                              (                                                                      X                  0                                                                              X                  1                                                            0                                            0                                                              X                  4                                                                              X                  5                                                            0                                            0                                            ⋯                                            ⋯                                                              X                                      M                    -                    4                                                                                                X                                      M                    -                    3                                                                              0                                            0                                                                                      -                                      X                    1                    *                                                                                                X                  0                  *                                                            0                                            0                                                              -                                      X                    5                    *                                                                                                X                  4                  *                                                            0                                            0                                            ⋯                                            ⋯                                                              -                                      X                                          M                      -                      3                                        *                                                                                                X                                      M                    -                    4                                    *                                                            0                                            0                                                                    0                                            0                                                              X                  2                                                                              X                  3                                                            0                                            0                                                              X                  6                                                                              X                  7                                                            ⋯                                            ⋯                                            0                                            0                                                              X                                      M                    -                    2                                                                                                X                                      M                    -                    1                                                                                                      0                                            0                                                              -                                      X                    3                    *                                                                                                X                  2                  *                                                            0                                            0                                                              -                                      X                    7                    *                                                                                                X                  6                  *                                                            ⋯                                            ⋯                                            0                                            0                                                              -                                      X                                          M                      -                      1                                        *                                                                                                X                                      M                    -                    2                                    *                                                              )                ,                            (        5        )            wherein the four rows are separately mapped onto M consecutive sub-carriers of four antennas. The block of M DFT samples Xk, k=0, 1, . . . , M−1 are the spectrum coefficients of one single carrier signal xk, k=0, 1, . . . , M−1. After the mapping, it can be observed that the signals mapped on each antenna are only part of the spectrum coefficients of the original single carrier signal xk, k=0, 1, . . . , M−1 (e.g. X0, X1, X4, X5, X8, X9, . . . , XM−4, XM−3 are mapped onto the first antenna), which implies that the transmitted signal on each antenna is not a single carrier signal. The loss of the single carrier property causes the PAPR of the signal to increase. The numerical evaluation of the increase in PAPR when employing the current SFBC+FSTD along with DFT-S-OFDM for the different antennas compared to a single carrier signal is shown in FIG. 4.
In another prior art solution, a space frequency coding scheme is proposed for SC-FDMA to preserve the single carrier property in the case of two transmit antennas. In this scheme, for a block of M DFT samples Xk, k=0, 1, . . . , M−1 of a time domain single carrier signal; first form pairs (k1,k2), where k1, k2 is the index of the DFT samples and k1=0, 1, 2, . . . M−1, k2=(M/2−k1) mod M; then perform SFBC between the k1-th sample Xk1 and the k2-th sample Xk2; SFBC is operated as
         (                                        X                          k              ⁢                                                          ⁢              1                                                            X                          k              ⁢                                                          ⁢              2                                                                        -                          X                              k                ⁢                                                                  ⁢                2                            *                                                            X                          k              ⁢                                                          ⁢              1                        *                                )  when k1 is odd, and as
         (                                        X                          k              ⁢                                                          ⁢              1                                                            X                          k              ⁢                                                          ⁢              2                                                                        X                          k              ⁢                                                          ⁢              2                        *                                                -                          X                              k                ⁢                                                                  ⁢                1                            *                                            )  when k1 is even. The encoding matrix on the block of M DFT samples is shown in matrix (6),
                              (                                                                      X                  0                                                                              X                  1                                                            ⋯                                            ⋯                                                              X                                                            M                      /                      2                                        -                    2                                                                                                X                                                            M                      /                      2                                        -                    1                                                                                                X                                      M                    /                    2                                                                                                X                                                            M                      /                      2                                        +                    1                                                                              ⋯                                            ⋯                                                              X                                      M                    -                    2                                                                                                X                                      M                    -                    1                                                                                                                        -                                      X                                                                  M                        /                        2                                            -                      1                                        *                                                                                                X                                                            M                      /                      2                                        -                    2                                    *                                                            ⋯                                            ⋯                                                              -                                      X                    1                    *                                                                                                X                  0                  *                                                                              -                                      X                                          M                      -                      1                                        *                                                                                                X                                      M                    -                    2                                    *                                                            ⋯                                            ⋯                                                              -                                      X                                                                  M                        /                        2                                            -                      1                                        *                                                                                                X                                      M                    /                    2                                    *                                                              )                .                            (        6        )            
The two rows are mapped onto the two transmit antennas, respectively. The proposed scheme enables the signals transmitted from two transmit antennas to have the same PAPR as a single carrier signal, but said scheme is only useful for two transmit antennas.
In a yet another prior art solution, a space-frequency transmit diversity scheme for four antenna SC-FDMA is proposed. The scheme is based on quasi-orthogonal space frequency block code for four antennas according to,
                              (                                                                      X                  0                                                                              X                  1                                                                              X                  2                                                                              X                  3                                                                                                      -                                      X                    1                    *                                                                                                X                  0                  *                                                                              -                                      X                    3                    *                                                                                                X                  2                  *                                                                                                      X                  2                                                                              X                  3                                                                              X                  0                                                                              X                  1                                                                                                      -                                      X                    3                    *                                                                                                X                  2                  *                                                                              -                                      X                    1                    *                                                                                                X                  0                  *                                                              )                .                            (        9        )                            If columns of one matrix can be divided into groups, wherein the columns within each group are not orthogonal to each other, but the columns from different groups are orthogonal to each other, then the matrix is called quasi-orthogonal. For the encoding matrix shown in (9) the four columns could be divided into two groups, wherein the first group includes the first column and the third column, and the second group includes the remaining two columns. It can be observed that the two columns in each group are not orthogonal, but the columns from two different groups are orthogonal to each other, and hence the encoding matrix (9) is a quasi-orthogonal matrix. The four rows of the quasi-orthogonal matrix defined in (9) represent four different transmit antennas, and the columns represent four sub-carriers, therefore said scheme is called quasi-orthogonal space frequency block code.In general, the above encoding matrix is repeated over every four sub-carrier to obtain the structure,        
                              (                                                                      X                  0                                                                              X                  1                                                                              X                  2                                                                              X                  3                                                                              X                  4                                                                              X                  5                                                                              X                  6                                                                              X                  7                                                            ⋯                                                              X                                      M                    -                    4                                                                                                X                                      M                    -                    3                                                                                                X                                      M                    -                    2                                                                                                X                                      M                    -                    1                                                                                                                        -                                      X                    1                    *                                                                                                X                  0                  *                                                                              -                                      X                    3                    *                                                                                                X                  2                  *                                                                              -                                      X                    5                    *                                                                                                X                  4                  *                                                                              -                                      X                    7                    *                                                                                                X                  6                  *                                                            ⋯                                                              -                                      X                                          M                      -                      3                                        *                                                                                                X                                      M                    -                    4                                    *                                                                              -                                      X                                          M                      -                      1                                        *                                                                                                X                                      M                    -                    2                                    *                                                                                                      X                  2                                                                              X                  3                                                                              X                  0                                                                              X                  1                                                                              X                  6                                                                              X                  7                                                                              X                  4                                                                              X                  5                                                            ⋯                                                              X                                      M                    -                    2                                                                                                X                                      M                    -                    1                                                                                                X                                      M                    -                    4                                                                                                X                                      M                    -                    3                                                                                                                        -                                      X                    3                    *                                                                                                X                  2                  *                                                                              -                                      X                    1                    *                                                                                                X                  0                  *                                                                              -                                      X                    7                    *                                                                                                X                  6                  *                                                                              -                                      X                    5                    *                                                                                                X                  4                  *                                                            ⋯                                                              -                                      X                                          M                      -                      1                                        *                                                                                                X                                      M                    -                    2                                    *                                                                              -                                      X                                          M                      -                      3                                        *                                                                                                X                                      M                    -                    4                                    *                                                              )                ,                            (        10        )            where X={X0, X1, . . . , XM−1} is a block of MDFT samples of a time domain single carrier signal. Regarding the signals transmitted from the four antennas in (10), only the signal transmitted from the first antenna is a single carrier signal. What has been done in this prior art solution is to make the signals transmitted from the remaining three antennas to be single carrier signals while preserving the quasi-orthogonal structure to achieve transmit diversity. Said prior art solution works as follows:    1. A block of M DFT samples X={X0, X1, . . . , XM−1}, which constitutes a first branch, is cyclically shifted with a cyclically shift size M/2 to obtain a block of DFT samples Y={Yk|Yk=X(k−M/2)modM, k=0, 1, . . . , M−1} which represents a third branch for quasi-orthogonal space frequency coding.    2. The block of M DFT samples X is reversed, cyclically shifted and conjugated, and then a minus sign is added on every other of the DFT samples to obtain a block of M DFT samples A which represents a second branch for quasi-orthogonal space frequency coding. Similarly, the same operations are performed on Y to obtain a block of M DFT samples B which represents a fourth branch for quasi-orthogonal space frequency coding.Finally, the four blocks of DFT samples X, A, Y, B are grouped as an encoding matrix,
                              (                                                                      X                  0                                                                              X                  1                                                            ⋯                                                              X                  k                                                            ⋯                                                              X                                      M                    -                    1                                                                                                                        A                  0                                                                              A                  1                                                            ⋯                                                              A                  k                                                            ⋯                                                              A                                      M                    -                    1                                                                                                                        Y                  0                                                                              Y                  1                                                            ⋯                                                              Y                  k                                                            ⋯                                                              Y                                      M                    -                    1                                                                                                                        B                  0                                                                              B                  1                                                            ⋯                                                              B                  k                                                            ⋯                                                              B                                      M                    -                    1                                                                                )                ⁢                                  ⁢        where        ⁢                                  ⁢                                            A              k                        =                                                            (                                      -                    1                                    )                                                  k                  +                  1                                            ⁢                              X                                                      (                                          p                      -                      1                      -                      k                                        )                                    ⁢                  mod                  ⁢                                                                          ⁢                  M                                *                                              ,                      k            =            0                    ,          1          ,          …          ⁢                                          ,                      M            -            1                          ⁢                                  ⁢                                            Y              k                        =                          X                                                (                                      k                    -                                          M                      /                      2                                                        )                                ⁢                mod                ⁢                                                                  ⁢                M                                              ,                      k            =            0                    ,          1          ,          …          ⁢                                          ,                      M            -            1                          ⁢                                  ⁢                                            B              k                        =                                                            (                                      -                    1                                    )                                                  k                  +                  1                                            ⁢                              Y                                                      (                                          p                      -                      1                      -                      k                                        )                                    ⁢                  mod                  ⁢                                                                          ⁢                  M                                *                                              ,                      k            =            0                    ,          1          ,          …          ⁢                                          ,                      M            -            1                    ,                                    (        11        )            and where the corresponding samples of the four columns,                k, (p−1−k) mod M, (k−M/2) mod M, (p−M/2−1−k) mod M,can be expressed by formula (12a) and (12b) below, where the formula (12a) corresponds to when k is an even number, and the formula (12b) corresponds to when k is an odd number, respectively,        
                              (                                                                      X                  k                                                                              X                                                            (                                              p                        -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              k                        -                                                  M                          /                          2                                                                    )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                                        -                                      X                                                                  (                                                  p                          -                          1                          -                          k                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                X                  k                  *                                                                              -                                      X                                                                  (                                                  p                          -                                                      M                            /                            2                                                    -                          1                          -                          k                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                X                                                            (                                              k                        -                                                  M                          /                          2                                                                    )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                                                      X                                                            (                                              k                        -                                                  M                          /                          2                                                                    )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                  k                                                                              X                                                            (                                              p                        -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                                        -                                      X                                                                  (                                                  p                          -                                                      M                            /                            2                                                    -                          1                          -                          k                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        3                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                              -                                      X                                                                  (                                                  p                          -                                                      M                            /                            2                                                    -                          1                          -                          k                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                              )                ,                            (                  12          ⁢                                          ⁢          a                )                                          (                                                                      X                  k                                                                              X                                                            (                                              p                        -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              k                        -                                                  M                          /                          2                                                                    )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                                        X                                                            (                                              p                        -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                              -                                      X                    k                    *                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                              -                                      X                                                                  (                                                  k                          -                                                      M                            /                            2                                                                          )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                                        X                                                            (                                              k                        -                                                  M                          /                          2                                                                    )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                X                  k                                                                              X                                                            (                                              p                        -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                                                                                                        X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                              -                                      X                                                                  (                                                  p                          -                                                      M                            /                            2                                                    -                          3                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                                X                                                            (                                              p                        -                                                  M                          /                          2                                                -                        1                        -                        k                                            )                                        ⁢                    mod                    ⁢                                                                                  ⁢                    M                                    *                                                                              -                                      X                                                                  (                                                  p                          -                                                      M                            /                            2                                                    -                          1                                                )                                            ⁢                      mod                      ⁢                                                                                          ⁢                      M                                        *                                                                                )                .                            (                  12          ⁢                                          ⁢          b                )            
It can be proved that the encoding matrices (12a) and (12b) satisfy the condition of quasi-orthogonal matrix. The difference between equations (10) and (11) is that the indices of the four samples used to create any quasi-orthogonal space-frequency coding matrix are not consecutive, but the quasi-orthogonal space-frequency coding structure is kept.
The structure proposed in the above prior art solution makes the signal transmitted from each antenna to have the property of a single carrier signal, while at the same time utilise the quasi-orthogonal space frequency coding structure to achieve transmit diversity. However, the disadvantage with quasi-orthogonal space frequency coding is the high increase in decoding complexity because inversion of a larger size matrix needs to be done. Another major drawback with this prior art solution is the performance loss in terms of Block Error Rate (BLER) compared with SFBC+FSTD.